purity-check

To check your Lean 4 proof environment for forbidden axioms, run a purity validation to detect external Mathlib imports, classical logic usage, and native decision procedures, ensuring strict compliance with core standards.

Axiom verification in formal proofs is the process of detecting unauthorized external axioms to maintain foundational purity. It is needed to ensure proof integrity and reliability by confirming the environment uses only a minimal, allowed set of axioms.

You cannot use classical logic and Mathlib imports if your project requires foundational purity. This verification detects and flags such external dependencies to ensure your formal proofs rely strictly on Lean 4 core standards.

The best way to ensure proof integrity before formal proof development in Lean 4 is to execute a purity check. This validates that your environment has zero external dependencies and adheres strictly to core axioms.

Detecting native decision procedures and external axioms automatically requires a dedicated verification check. This process scans your formal proof environment to identify forbidden elements and validate minimal axiom usage for foundational compliance.

Your formal proof fails purity compliance checks in Lean 4 if the environment includes forbidden external axioms, Mathlib imports, classical logic, or native decision procedures, violating the strict standards required for foundational integrity.